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Chapter 3: Problem 20

For each of the questions, four choices have been provided. Select the correct alternative. Which of the following sets of quantum numbers represent electron in hydrogen atom? (a) \(1,1,0,+1 / 2\) (b) \(1,0,0,+1 / 2\) (c) \(3,0,0,-1 / 2\) (d) \(4,2,1,-1 / 2\)

Short Answer

Expert verified
The correct sets of quantum numbers are: - Option (b): \(1,0,0,+1 / 2\) - Option (c): \(3,0,0,-1 / 2\) - Option (d): \(4,2,1,-1 / 2\)

Step by step solution

01

Option (a): \(1,1,0,+1 / 2\)

For this option, we have \(n=1\), \(l=1\), \(m_l=0\), and \(m_s=+1/2\). As per rule 2, since n=1, the value of l should be 0 (because l can range from 0 to n-1). But l=1 in this case, so option (a) is incorrect.
02

Option (b): \(1,0,0,+1 / 2\)

In this case, we have \(n=1\), \(l=0\), \(m_l=0\), and \(m_s=+1/2\). For n=1, l can be 0, and for l=0, m_l can be 0, according to rules 2 and 3. The m_s value of \(+1/2\) is also valid, as it follows rule 4. Thus, option (b) is correct.
03

Option (c): \(3,0,0,-1 / 2\)

For this case, we have \(n=3\), \(l=0\), \(m_l=0\), and \(m_s=-1/2\). For n=3, l can be 0 according to rule 2, and for l=0, m_l can be 0, satisfying rule 3 as well. The m_s value of \(-1/2\) is valid, following rule 4. So, option (c) is also correct.
04

Option (d): \(4,2,1,-1 / 2\)

In this case, we have \(n=4\), \(l=2\), \(m_l=1\), and \(m_s=-1/2\). For n=4, l can be 2, according to rule 2, and for l=2, m_l can range from -2 to 2, so m_l=1 is valid, following rule 3. The m_s value of \(-1/2\) satisfies rule 4 as well. Thus, option (d) is also correct. In conclusion, the sets of quantum numbers that represent an electron in a hydrogen atom are (b), (c), and (d).

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